Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9001	2^196101-175	59033	Lelio R Paula	04/2011
9002	2^196085+5775	59028	Lelio R Paula	05/2011
9003	2^196034+11715	59013	Lelio R Paula	05/2011
9004	2^196018-18485	59008	Enzo Doria	05/2013
9005	2^195984-2163	58998	Yves Minet	08/2013
9006	3^123645-16	58994	Lelio R Paula	10/2012
9007	39^37078-38	58994	Norbert Schneider	05/2014
9008	2^195958-16853	58990	Enzo Doria	05/2013
9009	2^195930-3071	58981	Yves Minet	10/2014
9010	2^195924+513	58980	Lelio R Paula	05/2011
9011	2^195863+155	58961	Lelio R Paula	04/2011
9012	(28*10^58956+113)/3	58957	Robert Price	03/2016
9013	11^56612-9300	58956	Enzo Doria	02/2013
9014	2^195833-17173	58952	Enzo Doria	05/2013
9015	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
9016	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
9017	139^27504-138	58942	Norbert Schneider	10/2015
9018	a(222666)	58929	Robert Price	05/2019
9019	(418*10^58923+23)/9	58925	Robert Price	08/2017
9020	3^123495+44	58923	Lelio R Paula	10/2012
9021	2^195737-18565	58923	Enzo Doria	05/2013
9022	79185!6-16	58921	Robert Price	08/2018
9023	14^51407+47	58920	Lelio R Paula	03/2013
9024	2^195691-99	58909	Lelio R Paula	04/2011
9025	2^195667-1859827	58902	Enzo Doria	04/2016
9027	2^195642+75499	58895	Enzo Doria	04/2016
9026	(299*10^58893+1)/3	58895	Robert Price	11/2017
9028	8*6^75678+5	58890	Lelio R Paula	09/2014
9029	14222^13827+13827^14222	58890	Hans Havermann	05/2019
9031	2^195618+73189	58887	Enzo Doria	04/2016
9030	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
9032	t(197953)	58881	Robert Price	12/2014
9033	2^195581-16105	58876	Enzo Doria	04/2013
9034	(8*10^58872+67)/3	58873	Robert Price	01/2017
9035	7*2^195542-5	58865	Lelio R Paula	03/2014
9036	2*10^58861+9^58861	58862	Mike Oakes	04/2011
9037	11^56513-1620	58853	Enzo Doria	11/2012
9038	2^195496+165	58851	Lelio R Paula	04/2011
9039	5^84187+66	58845	Lelio R Paula	10/2012
9040	2^195478-4991	58845	Yves Minet	05/2019
9041	(28*10^58843-43)/3	58844	Robert Price	04/2016
9042	2^195462-17565	58840	Enzo Doria	05/2013
9043	2^195449-4171	58837	Yves Minet	02/2018
9044	2^195435+59273	58832	Yves Minet	01/2011
9045	2^195424-18605	58829	Enzo Doria	05/2013
9046	10295^14658-14658^10295	58818	Norbert Schneider	03/2019
9047	2^195385-111	58817	Lelio R Paula	04/2011
9048	7*10^58815-83	58816	Robert Price	09/2017
9049	10130^14683-14683^10130	58815	Norbert Schneider	03/2019
9050	2^195357-4303	58809	Yves Minet	08/2018
9051	14218^13631+13631^14218	58785	Hans Havermann	05/2019
9052	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
9053	2^195207-18109	58764	Enzo Doria	05/2013
9054	2^195199-1567	58761	Yves Minet	08/2012
9055	2^195190+73759	58759	Enzo Doria	04/2016
9056	9*7^69525-4	58757	Lelio R Paula	09/2014
9057	2^195170-18045	58753	Enzo Doria	05/2013
9058	2^195166-165	58751	Lelio R Paula	04/2011
9059	(754*10^58748-7)/9	58750	Robert Price	11/2017
9060	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
9061	7*3^123109-2	58739	Lelio R Paula	04/2014
9062	(8*10^58738-611)/9	58738	Robert Price	11/2017
9063	18^46790+77	58735	Lelio R Paula	03/2013
9065	2^195095-337297	58730	Gary Barnes	09/2009
9064	(14*10^58729+31)/9	58730	Robert Price	02/2015
9066	99^29424+98	58720	Norbert Schneider	07/2013
9067	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
9068	2^195001-69	58702	Lelio R Paula	04/2011
9069	2^194978-487811	58695	Gary Barnes	09/2009
9070	163^26530+26530^163	58690	Serge Batalov	05/2014
9071	2^194940-194940+1	58683	Robert Price	10/2014
9072	(76*10^58669+41)/9	58670	Robert Price	10/2015
9073	14^51186+87	58666	Lelio R Paula	03/2013
9074	2^194878-97305	58665	Lelio R Paula	09/2011
9075	5^83927-18136	58663	Enzo Doria	05/2014
9076	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
9077	7^69411+40	58660	Lelio R Paula	10/2012
9078	6^75382-79	58659	Lelio R Paula	10/2012
9079	2^194854+27	58657	Lelio R Paula	04/2011
9080	2^194801+29835	58641	Lelio R Paula	10/2012
9081	2^194752+195	58627	Lelio R Paula	04/2011
9082	7^69371-6^69371	58626	Predrag Minovic	08/2004
9083	2^194747-112519	58625	Enzo Doria	06/2014
9084	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
9085	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
9086	10^58608+55273	58609	Patrick De Geest	07/2017
9087	10^58608-800001	58608	Robert Price	06/2017
9088	10^58608-60119	58608	Patrick De Geest	07/2017
9089	5^83836+76	58599	Lelio R Paula	10/2012
9090	18^46664+31	58577	Lelio R Paula	03/2013
9091	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
9092	2^194574+165	58573	Lelio R Paula	04/2011
9095	2^194569-12211	58572	Enzo Doria	06/2014
9093	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
9094	10^58571+202837	58572	Patrick De Geest	02/2017
9096	(10^58571+41)/3	58571	Robert Price	01/2017
9097	10^58571-343629	58571	Patrick De Geest	02/2017
9098	(43*10^58563-403)/9	58564	Robert Price	04/2017
9099	11^56235-7950	58563	Enzo Doria	02/2013
9100	145^27095-144	58563	Norbert Schneider	11/2018
9101	2^194505-4615	58552	Yves Minet	05/2019
9102	(14*10^58550+211)/9	58551	Robert Price	11/2017
9103	2^194479-113239	58545	Enzo Doria	07/2014
9104	2^194455-112249	58537	Enzo Doria	06/2014
9105	2^194405-111919	58522	Enzo Doria	05/2014
9106	(4*10^58521-19)/3	58522	Robert Price	06/2017
9108	(7^69247-4^69247)/3	58521	Robert Price	06/2012
9107	5*7^69246+8	58521	Lelio R Paula	09/2014
9109	2^194358-1167	58508	Lelio R Paula	05/2011
9110	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
9111	15091^7518+7518^15091	58495	Hans Havermann	04/2019
9112	15852^4895+4895^15852	58490	Hans Havermann	04/2019
9113	(493*10^58486-7)/9	58488	Robert Price	07/2016
9114	3^122579-340	58486	Lelio R Paula	10/2012
9115	(11*10^58458-149)/3	58459	Robert Price	01/2017
9116	(47*10^58456+133)/9	58457	Robert Price	04/2017
9117	2^194186+85	58456	Lelio R Paula	04/2011
9118	3^122506-2^(122506-1)	58451	Robert Price	01/2016
9119	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
9120	177^25998-2	58443	Lelio R Paula	10/2017
9121	15^49690-26	58440	Lelio R Paula	03/2013
9122	10^58437+110721	58438	Patrick De Geest	12/2012
9123	10^58437-11	58437	Robert Price	05/2011
9124	2^194095+69	58429	Lelio R Paula	04/2011
9125	(29*10^58417-77)/3	58418	Robert Price	01/2017
9126	2^194034+177	58411	Lelio R Paula	04/2011
9127	789^20158+20158^789	58400	Norbert Schneider	06/2016
9128	14^50949+75	58395	Lelio R Paula	03/2013
9129	2^193974-114761	58392	Enzo Doria	05/2015
9130	2^193965+5	58390	Henri Lifchitz	12/2002
9131	(5*10^58384-29)/3	58385	Robert Price	02/2017
9132	3^122360+80	58381	Lelio R Paula	10/2012
9133	10103^14577-114	58373	Enzo Doria	07/2012
9134	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
9135	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
9136	11^56041-1560	58361	Enzo Doria	11/2012
9137	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
9138	3^122313+58	58359	Lelio R Paula	10/2012
9139	6^74996-119	58359	Lelio R Paula	10/2012
9140	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
9141	2^193861-112255	58358	Enzo Doria	06/2014
9142	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
9143	18^46487+37	58354	Lelio R Paula	03/2013
9144	17^47419+54	58347	Lelio R Paula	03/2013
9145	2^193812-4799	58344	Yves Minet	05/2019
9146	15486^5851+5851^15486	58340	Hans Havermann	04/2019
9147	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
9148	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
9149	14088^13825+13825^14088	58334	Hans Havermann	04/2019
9150	144^27025-143	58330	Norbert Schneider	11/2018
9151	11900^14311-14311^11900	58326	Norbert Schneider	05/2019
9152	15297^6494+6494^15297	58321	Hans Havermann	04/2019
9153	16293^3794+3794^16293	58315	Hans Havermann	04/2019
9154	3^122219-2^122219	58314	Mike Oakes	09/2003
9155	(199*10^58306+11)/3	58308	Robert Price	05/2017
9156	2^193674-18825	58302	Lelio R Paula	05/2011
9157	14897^8172+8172^14897	58282	Hans Havermann	04/2019
9158	5*10^58275+3	58276	Dmitry Domanov	11/2010
9159	2^193578-112913	58273	Enzo Doria	06/2014
9160	2^193541+1299	58262	Lelio R Paula	05/2011
9161	10^58250+93	58251	Robert Price	01/2011
9162	10^58250-175607	58250	Patrick De Geest	12/2012
9163	(107^28703+1)/108	58248	Richard Fischer	05/2018
9164	2^193492+8415	58247	Lelio R Paula	10/2012
9165	2^193444+157	58233	Lelio R Paula	04/2011
9166	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
9167	2^193430-111881	58229	Enzo Doria	05/2014
9168	10^58225+124579	58226	Patrick De Geest	12/2012
9169	10^58225-93	58225	Robert Price	05/2011
9170	2^193375-295	58212	Yves Minet	05/2013
9171	14018^14037-14037^14018	58208	Norbert Schneider	10/2018
9172	2^193345+77267	58203	Enzo Doria	05/2016
9173	21^44017-20^44017	58201	Robert Price	05/2012
9174	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
9175	17^47291+20	58190	Lelio R Paula	03/2013
9176	p(12528)#/2-128	58170	Robert Price	05/2017
9177	2^193214-135	58164	Lelio R Paula	04/2011
9178	19^45483-80	58162	Lelio R Paula	03/2013
9179	(4*10^58155+83)/3	58156	Robert Price	01/2017
9181	14^50739-13	58154	Lelio R Paula	03/2013
9180	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
9182	(2*10^58151+457)/9	58151	Robert Price	01/2017
9183	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
9184	14555^9874+9874^14555	58140	Hans Havermann	05/2019
9185	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
9187	2^193091-1237	58127	Yves Minet	08/2012
9186	9*7^68780-2	58127	Lelio R Paula	09/2014
9188	2473^17130+17130^2473	58126	Norbert Schneider	10/2018
9189	2^193083-869688105	58124	Lelio R Paula	10/2012
9190	2^193058-45	58117	Lelio R Paula	04/2011
9191	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
9192	11^55795-42	58105	Lelio R Paula	03/2013
9193	3^121779-16	58104	Lelio R Paula	10/2012
9194	(13*10^58103+191)/3	58104	Robert Price	08/2017
9195	15865^4594+4594^15865	58101	Hans Havermann	05/2019
9196	2^192986+195	58095	Lelio R Paula	04/2011
9197	7^68740+2*3^68740	58093	Mike Oakes	07/2010
9198	(85*10^58091-1)/3	58093	Robert Price	07/2017
9199	(404*10^58087-53)/9	58089	Robert Price	11/2017
9200	12^53821+11	58083	Lelio R Paula	02/2013
9201	119^27979-118	58072	Norbert Schneider	10/2013
9202	14380^10899+10899^14380	58058	Hans Havermann	04/2019
9203	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
9204	2^192808-1127	58041	Yves Minet	05/2013
9205	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
9206	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
9207	3*10^58032-23	58033	Robert Price	11/2017
9208	2^192678+72943	58002	Enzo Doria	04/2016
9209	(13*10^57997-37)/3	57998	Robert Price	08/2017
9210	2^192657-3189	57996	Yves Minet	10/2014
9211	6^74525-149	57992	Lelio R Paula	10/2012
9212	42^35723-41	57988	Norbert Schneider	06/2014
9213	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
9214	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
9215	(2^192596-5)/139	57976	Lelio R Paula	02/2012
9216	10^57975+67833	57976	Patrick De Geest	09/2013
9217	10^57975-47693	57975	Patrick De Geest	09/2013
9218	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
9219	14025^13592+13592^14025	57970	Hans Havermann	04/2019
9220	(29*10^57967+673)/9	57968	Robert Price	10/2017
9221	(3^121492-5)/4	57966	Lelio R Paula	03/2012
9222	2^192549+35	57964	Lelio R Paula	04/2011
9223	28799!2+2	57962	Robert Price	10/2012
9224	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
9225	11108^14323-14323^11108	57946	Norbert Schneider	05/2019
9226	7001^15069-100	57943	Enzo Doria	07/2012
9227	L(277273)/11090921	57940	Donovan Johnson	11/2005
9228	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
9229	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
9230	12752^14111-14111^12752	57934	Norbert Schneider	01/2019
9231	2^192443+1385	57932	Lelio R Paula	05/2011
9232	132^27317-131	57928	Norbert Schneider	03/2015
9233	41522!3-59049	57912	Robert Price	12/2015
9234	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
9235	2^192339-2515	57900	Yves Minet	07/2014
9236	2^192303+7695	57889	Lelio R Paula	10/2012
9237	2^192273-5955	57880	Lelio R Paula	05/2011
9238	2^192257+16095	57876	Lelio R Paula	05/2011
9239	109^28401-2	57865	Lelio R Paula	10/2017
9240	2^192218-111861	57864	Enzo Doria	05/2014
9241	2^192214-3941	57863	Yves Minet	04/2017
9242	(2^192212+3)/259	57860	Lelio R Paula	02/2012
9243	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
9244	80^30393-79	57841	Norbert Schneider	03/2015
9245	20^44455-3123	57838	Enzo Doria	03/2013
9246	2^192122-195	57835	Lelio R Paula	04/2011
9247	(29*10^57834+91)/3	57835	Robert Price	03/2016
9248	8*6^74306+5	57823	Lelio R Paula	09/2014
9249	(39^36341-1)/38	57820	Robert Price	04/2012
9250	2^192037-111805	57809	Enzo Doria	05/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)